How to use the array function
The first thing you want to do is to have a starting object that is more than just a line. The array modifier will take your object and duplicate it with some offset. Thus, what you would've ended up with (in the case that the array was setup properly), would be 48 lines without any planes.

Add a Mesh > Circle with 48*4 = 192 vertices. Then, select all of the circle's vertices except for two adjacent ones (that you want to keep) in Edit Mode, press ALt+M > Merge at Center. This will create the center vertex. Join the two perimeter vertices by selecting them and pressing F, then select everything with A, and press F again to fill in the triangle.

Then, add in the Array modifier to the triangle. Disable the Relative Offset, and enable the Object Offset as you did in your attached file. Add the Empty Axis, and rotate it in the Z-axis by 90/48 = 1.875 degrees.

Use the empty for the Object Offset in the Array modifier, and you've now gotten a quarter circle made up of 48 triangles.



Edit:

From your blend file, the reason why your array isn't working properly is that you have an unapplied rotation to the "Circle" object. Select the circle object and press Ctrl+A and select Apply > Rotation. Your array works fine after that step.